It's all about energy. The 9mm Luger has a more powerful charge. A .357 Magnum is a vastly more powerful round but it's a smaller bullet. The 380 is a relatively anemic round. A 38 special is better, a 9mm is better than that. A a 357 magnum is probably the best "man killer" as more powerful rounds like the 44 magnum, .460, .480 etc. over penetrate. Shot placement is very important and I wouldn't want to get hit with any of that, but with enough winter clothing a 380 or a 32 might just piss off a big guy.
Both the .380 and 9mm use bullets of .355 inch diameter. The .38 special uses the same .357 diameter bullets as the .357 magnum.